Final answer:
The most common residential scale factor used is 1/4, representing a proportion where 1 unit in the model corresponds to 4 actual units. To find the actual dimensions from a scale model, you set up and solve a proportion using the scale factor.
Step-by-step explanation:
The most common residential scale factor used is 1/4. This means that one unit on the drawing or model represents four units on the actual structure. When applying this information to solve problems, we set up proportions where the scale dimension is compared to the actual dimension. For example, if the scale factor is 1:4 and the scale dimension is 4, then we can set up the proportion 1:4=4:x to find the actual dimension x.
To figure out each scale factor, you compare the model or drawing measurement to the actual measurement, writing them as ratios. For instance, if a drawing measures 2 inches while the actual object measures 8 feet, the scale factor is 2 inches to 8 feet. Solving this involves converting both measurements to the same units and simplifying the ratio. Example: A drawing of a box has dimensions that are 2 inches by 3 inches by 5 inches. If the actual box's dimensions are 3(1/4) times larger, we would multiply each dimension by 3.25 to find the actual dimensions.